Dear colleague,

       Some time ago we sent you a subroutine for the results of the
relativistic thermal bremsstrahlung Gaunt factor. Our paper "RELATIVISTIC
THERMAL BREMSSTRAHLUNG GAUNT FACTOR FOR THE INTRACLUSTER
PLASMA. II. ANALYTIC FITTING FORMULAE" has been published in ApJ
Supplement 128: 125-138, 2000 May. In this work we presented analytic
fitting formulae for Z = 1 - 28.

       We have added the analytic fitting formulae for Z = 29, 30. Here with we
are sending you an updated subroutine for Z = 1 - 30. We hope this would
be helpful for your research.

       We would most like to appreciate whatever comment you might have on
our work.

With my best wishes,

Naoki Itoh


Naoki Itoh
Department of Physics, Sophia University
  7    -1, Kioi-cho, Chiyoda-ku, Tokyo 102-8554 Japan
Telephone  81 (0)3 3238 3431
Telefax      81 (0)3 3238 3341


CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C                                                                    C
C     THERMAL BREMSSTRAHLUNG GAUNT FACTOR ANALYTIC FITTING FORMULA   C
C                                                                    C
C            GF = sum{ T^i * U^j }, { i,j = 0 - 10 }.                C
C                                                                    C
C     This formula is available for -4 <log u <1,  6 <log T <8.5,    C
C           &    1 <Z <30                                            C
C                                                                    C
C     Insert the coefficients from DATA FILE.                        C
C     The coefficients are arranged in Aij = A00, A01, A02, ...      C
C                                                                    C
C                             28th Feb. 2001 Li-Da- Group (^_^)      C
C                                                                    C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
       IMPLICIT REAL*8 (A-H, O-Z)
       REAL*8 A(121)

C     in the case of Z=1

       DATA A/
      *2.42979D+00,-2.86499D+00,4.99579D-01,3.43156D-01,-4.18944D-02,
      *-5.68063D-02,1.74588D-01,2.68556D-02,-1.53561D-01,-1.50817D-02,
      *4.48156D-02,-1.88711D-02,-2.16925D-01,-2.41059D-01,1.80971D-01,
      *4.48744D-01,-1.95323D-01,-2.53964D-01,3.00024D-01,-6.83477D-03,
      *-1.52541D-01,3.91975D-02,9.34182D-03,1.86384D-01,1.21854D-01,
      *-1.37451D-01,-8.23360D-01,-4.72693D-01,2.98602D+00,9.55789D-01,
      *-3.84957D+00,-4.78813D-01,1.61382D+00,9.12597D-02,-1.34722D-01,
      *-2.75406D-01,-8.52425D-01,9.45650D-01,3.68253D+00,-1.75533D+00,
      *-4.88239D+00,1.57378D+00,2.10176D+00,-5.21118D-01,-1.02245D-01,
      *-4.46492D-01,2.57659D-01,1.11846D+00,4.93886D+00,2.22436D+00,
      *-2.12164D+01,-6.02085D+00,2.73997D+01,3.25013D+00,-1.13785D+01,
      *-1.52040D-01,2.90882D-01,9.68053D-01,2.00368D+00,-4.34255D+00,
      *-9.48579D+00,7.65932D+00,1.30380D+01,-6.03848D+00,-5.70148D+00,
      *1.76429D+00,1.37061D-01,1.10173D+00,-5.55546D-01,-2.24507D+00,
      *-1.19797D+01,-6.40743D+00,5.16650D+01,1.56067D+01,-6.69150D+01,
      *-8.23744D+00,2.78509D+01,1.98974D-01,-3.00431D-01,-1.23622D+00,
      *-2.22406D+00,5.49768D+00,1.03009D+01,-9.24220D+00,-1.41964D+01,
      *6.77552D+00,6.24736D+00,-1.79388D+00,-8.54105D-02,-1.19625D+00,
      *4.17137D-01,2.10596D+00,1.29195D+01,7.30422D+00,-5.43550D+01,
      *-1.68713D+01,7.00780D+01,8.79718D+00,-2.91277D+01,-8.26964D-02,
      *1.09680D-01,5.34604D-01,8.94099D-01,-2.30457D+00,-4.01604D+00,
      *3.69866D+00,5.51504D+00,-2.53101D+00,-2.42607D+00,6.07045D-01,
      *2.13046D-02,4.58548D-01,-1.06446D-01,-7.52781D-01,-5.00532D+00,
      *-2.81808D+00,2.05954D+01,6.38161D+00,-2.64212D+01,-3.30777D+00,
      *1.09661D+01/

C     UI = log u, TI = log T

       DO 10 UI = -4.d0, 1.01d0, 0.1d0
          U = ( UI + 1.5d0 )/2.5d0

          DO 20 TI = 6.d0, 8.5d0, 0.1d0
             T = ( TI - 7.25d0 )/1.25d0


       GF = A(1) +A(2)*U +A(3)*U**2 +A(4)*U**3 +A(5)*U**4
      *     +A(6)*U**5+A(7)*U**6 +A(8)*U**7 +A(9)*U**8
      *     +A(10)*U**9 +A(11)*U**10
      *     +( A(12)+A(13)*U+A(14)*U**2+A(15)*U**3+A(16)*U**4
      *     +A(17)*U**5+A(18)*U**6+A(19)*U**7 +A(20)*U**8
      *     +A(21)*U**9 +A(22)*U**10 )*T
      *     +( A(23)+A(24)*U+A(25)*U**2+A(26)*U**3+A(27)*U**4
      *     +A(28)*U**5+A(29)*U**6+A(30)*U**7 +A(31)*U**8
      *     +A(32)*U**9 +A(33)*U**10 )*T**2
      *     +( A(34)+A(35)*U+A(36)*U**2+A(37)*U**3+A(38)*U**4
      *     +A(39)*U**5+A(40)*U**6+A(41)*U**7 +A(42)*U**8
      *     +A(43)*U**9 +A(44)*U**10 )*T**3
      *     +( A(45)+A(46)*U+A(47)*U**2+A(48)*U**3+A(49)*U**4
      *     +A(50)*U**5+A(51)*U**6+A(52)*U**7 +A(53)*U**8
      *     +A(54)*U**9 +A(55)*U**10 )*T**4
      *     +( A(56)+A(57)*U+A(58)*U**2+A(59)*U**3+A(60)*U**4
      *     +A(61)*U**5+A(62)*U**6+A(63)*U**7 +A(64)*U**8
      *     +A(65)*U**9 +A(66)*U**10 )*T**5
      *     +( A(67)+A(68)*U+A(69)*U**2+A(70)*U**3+A(71)*U**4
      *     +A(72)*U**5+A(73)*U**6+A(74)*U**7 +A(75)*U**8
      *     +A(76)*U**9 +A(77)*U**10 )*T**6
      *     +( A(78)+A(79)*U+A(80)*U**2+A(81)*U**3+A(82)*U**4
      *     +A(83)*U**5+A(84)*U**6+A(85)*U**7 +A(86)*U**8
      *     +A(87)*U**9 +A(88)*U**10 )*T**7
      *     +( A(89)+A(90)*U+A(91)*U**2+A(92)*U**3+A(93)*U**4
      *     +A(94)*U**5+A(95)*U**6+A(96)*U**7 +A(97)*U**8
      *     +A(98)*U**9 +A(99)*U**10 )*T**8
      *     +( A(100)+A(101)*U+A(102)*U**2+A(103)*U**3+A(104)*U**4
      *     +A(105)*U**5+A(106)*U**6+A(107)*U**7+A(108)*U**8
      *     +A(109)*U**9+A(110)*U**10)*T**9
      *     +( A(111)+A(112)*U+A(113)*U**2+A(114)*U**3+A(115)*U**4
      *     +A(116)*U**5+A(117)*U**6+A(118)*U**7+A(119)*U**8
      *     +A(120)*U**9+A(121)*U**10)*T**10

          write(6,*)UI,TI,GF

  20      CONTINUE
  10      CONTINUE

       STOP
       END

CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C                                                                    C
C     DATA FILE / The coefficients Z = 1 - 30                        C
C                                                                    C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C     Z=1
       DATA A/
      *2.42979D+00,-2.86499D+00,4.99579D-01,3.43156D-01,-4.18944D-02,
      *-5.68063D-02,1.74588D-01,2.68556D-02,-1.53561D-01,-1.50817D-02,
      *4.48156D-02,-1.88711D-02,-2.16925D-01,-2.41059D-01,1.80971D-01,
      *4.48744D-01,-1.95323D-01,-2.53964D-01,3.00024D-01,-6.83477D-03,
      *-1.52541D-01,3.91975D-02,9.34182D-03,1.86384D-01,1.21854D-01,
      *-1.37451D-01,-8.23360D-01,-4.72693D-01,2.98602D+00,9.55789D-01,
      *-3.84957D+00,-4.78813D-01,1.61382D+00,9.12597D-02,-1.34722D-01,
      *-2.75406D-01,-8.52425D-01,9.45650D-01,3.68253D+00,-1.75533D+00,
      *-4.88239D+00,1.57378D+00,2.10176D+00,-5.21118D-01,-1.02245D-01,
      *-4.46492D-01,2.57659D-01,1.11846D+00,4.93886D+00,2.22436D+00,
      *-2.12164D+01,-6.02085D+00,2.73997D+01,3.25013D+00,-1.13785D+01,
      *-1.52040D-01,2.90882D-01,9.68053D-01,2.00368D+00,-4.34255D+00,
      *-9.48579D+00,7.65932D+00,1.30380D+01,-6.03848D+00,-5.70148D+00,
      *1.76429D+00,1.37061D-01,1.10173D+00,-5.55546D-01,-2.24507D+00,
      *-1.19797D+01,-6.40743D+00,5.16650D+01,1.56067D+01,-6.69150D+01,
      *-8.23744D+00,2.78509D+01,1.98974D-01,-3.00431D-01,-1.23622D+00,
      *-2.22406D+00,5.49768D+00,1.03009D+01,-9.24220D+00,-1.41964D+01,
      *6.77552D+00,6.24736D+00,-1.79388D+00,-8.54105D-02,-1.19625D+00,
      *4.17137D-01,2.10596D+00,1.29195D+01,7.30422D+00,-5.43550D+01,
      *-1.68713D+01,7.00780D+01,8.79718D+00,-2.91277D+01,-8.26964D-02,
      *1.09680D-01,5.34604D-01,8.94099D-01,-2.30457D+00,-4.01604D+00,
      *3.69866D+00,5.51504D+00,-2.53101D+00,-2.42607D+00,6.07045D-01,
      *2.13046D-02,4.58548D-01,-1.06446D-01,-7.52781D-01,-5.00532D+00,
      *-2.81808D+00,2.05954D+01,6.38161D+00,-2.64212D+01,-3.30777D+00,
      *1.09661D+01/
C     Z=2
       DATA A/
      *2.43018D+00,-2.72345D+00,6.53244D-01,3.20441D-01,-2.38429D-01,
      *-2.12832D-01,2.00668D-01,1.61491D-01,-8.57469D-02,-4.75630D-02,
      *1.66734D-02,3.18447D-02,-3.69946D-01,-4.35144D-01,6.12665D-02,
      *6.28183D-01,1.59698D-01,-5.92434D-01,3.06090D-02,5.51209D-01,
      *-7.50336D-02,-2.36699D-01,-1.36511D-01,1.86195D-01,4.04170D-01,
      *5.90473D-01,-6.54710D-01,-1.86120D+00,6.71743D-01,2.22473D+00,
      *-3.07633D-01,-9.44580D-01,1.20284D-02,1.28409D-01,2.51376D-01,
      *6.20160D-01,-2.12638D+00,-5.20023D+00,5.15321D+00,1.32814D+01,
      *-5.42608D+00,-1.41340D+01,2.06330D+00,5.36417D+00,3.12032D-01,
      *-3.15528D-01,-1.55097D+00,-3.89762D+00,4.82155D+00,1.54232D+01,
      *-4.74722D+00,-2.01548D+01,5.70024D-01,8.69176D+00,8.68054D-01,
      *-6.27157D-02,-9.39514D-01,-1.92714D+00,7.13246D+00,1.66775D+01,
      *-1.81139D+01,-4.38396D+01,1.90438D+01,4.69143D+01,-7.12435D+00,
      *-1.77403D+01,-7.32389D-01,2.57734D-01,2.90231D+00,1.15635D+01,
      *-7.39508D+00,-4.26394D+01,2.35841D+00,5.47756D+01,7.56836D+00,
      *-2.34125D+01,-5.30361D+00,-1.97011D-02,1.27892D+00,2.49835D+00,
      *-8.61105D+00,-2.05150D+01,2.17460D+01,5.33622D+01,-2.28362D+01,
      *-5.68566D+01,8.54026D+00,2.14476D+01,7.25455D-01,1.19328D-01,
      *-2.40613D+00,-1.37882D+01,3.84819D+00,4.82621D+01,6.03324D+00,
      *-6.08902D+01,-1.59956D+01,2.57998D+01,8.35935D+00,3.35761D-02,
      *-5.69408D-01,-1.08181D+00,3.52091D+00,8.57917D+00,-8.76286D+00,
      *-2.20502D+01,9.15036D+00,2.33662D+01,-3.40816D+00,-8.78451D+00,
      *-2.53349D-01,-1.55129D-01,7.35601D-01,5.63159D+00,-3.72771D-01,
      *-1.90841D+01,-4.64385D+00,2.37796D+01,8.27763D+00,-1.00071D+01,
      *-3.92613D+00/
C     Z=3
       DATA A/
      *2.40975D+00,-2.60977D+00,7.80382D-01,3.56224D-01,-3.07763D-01,
      *-3.76640D-01,8.06517D-02,2.71201D-01,5.10339D-02,-7.23001D-02,
      *-2.22602D-02,1.16022D-01,-4.42185D-01,-4.97155D-01,-1.41147D-01,
      *3.23017D-01,4.60350D-01,-1.30098D-02,-2.14008D-01,1.76547D-01,
      *3.46920D-02,-1.55264D-01,-1.69447D-01,-7.08144D-02,2.38109D-02,
      *1.13137D+00,1.64742D+00,-1.83066D+00,-4.52334D+00,1.22365D+00,
      *5.24264D+00,-2.31565D-01,-2.23280D+00,-2.51538D-02,4.07142D-01,
      *1.08965D+00,-1.39549D-01,-5.70461D+00,-2.20564D+00,1.23167D+01,
      *4.10689D+00,-1.23765D+01,-2.13249D+00,4.67728D+00,2.04256D-02,
      *1.48913D+00,5.39570D-01,-8.19381D+00,-1.21877D+01,1.64207D+01,
      *3.95731D+01,-1.20533D+01,-4.90389D+01,2.23787D+00,2.11590D+01,
      *4.09184D-01,-1.10850D+00,-3.79855D+00,-2.28792D-01,2.13120D+01,
      *8.73122D+00,-4.55837D+01,-1.51762D+01,4.30987D+01,7.46992D+00,
      *-1.50447D+01,3.15197D-01,-4.34569D+00,-2.93636D+00,2.01544D+01,
      *3.76836D+01,-3.85034D+01,-1.14731D+02,2.63104D+01,1.38389D+02,
      *-3.72797D+00,-5.86407D+01,-5.82108D-01,1.10407D+00,5.11406D+00,
      *1.69949D+00,-2.74686D+01,-1.32737D+01,5.69884D+01,2.01252D+01,
      *-5.16248D+01,-9.15098D+00,1.70287D+01,-5.47274D-01,4.85466D+00,
      *4.49348D+00,-2.02995D+01,-4.59946D+01,3.66801D+01,1.32638D+02,
      *-2.31357D+01,-1.55497D+02,2.23637D+00,6.46247D+01,2.56293D-01,
      *-3.64181D-01,-2.25896D+00,-1.20859D+00,1.16892D+01,6.42960D+00,
      *-2.35848D+01,-8.87148D+00,2.06108D+01,3.78807D+00,-6.46175D+00,
      *2.62853D-01,-1.86090D+00,-2.10464D+00,7.23503D+00,1.91027D+01,
      *-1.24579D+01,-5.30289D+01,7.28296D+00,6.07675D+01,-3.79695D-01,
      *-2.48316D+01/
C     Z=4
       DATA A/
      *2.37989D+00,-2.52395D+00,8.73182D-01,4.10816D-01,-2.83752D-01,
      *-4.75682D-01,-1.20963D-01,2.79488D-01,2.28546D-01,-5.25988D-02,
      *-7.53209D-02,1.88841D-01,-4.42757D-01,-4.95574D-01,-2.99372D-01,
      *7.01433D-02,4.76958D-01,2.56778D-01,-8.58480D-02,4.24535D-02,
      *-3.39101D-02,-1.06008D-01,-1.63759D-01,-4.94494D-02,-4.12004D-01,
      *1.52733D-01,2.54857D+00,8.64698D-01,-4.75089D+00,-1.32412D+00,
      *4.31900D+00,5.47022D-01,-1.53821D+00,-7.49846D-02,-8.75525D-02,
      *1.20180D+00,2.80578D+00,-3.95021D+00,-8.47484D+00,6.69196D+00,
      *9.72016D+00,-5.82093D+00,-3.90203D+00,1.97415D+00,-2.40134D-01,
      *7.86343D-01,3.63367D+00,-1.50540D-01,-2.18460D+01,-6.48003D+00,
      *4.86375D+01,1.18225D+01,-4.72114D+01,-5.84463D+00,1.67929D+01,
      *4.10230D-01,9.19773D-01,-4.29388D+00,-1.19308D+01,1.68168D+01,
      *3.70300D+01,-2.96340D+01,-4.40601D+01,2.48256D+01,1.80053D+01,
      *-8.01276D+00,1.00744D+00,-1.41250D+00,-1.16507D+01,-5.96521D+00,
      *6.62294D+01,3.41385D+01,-1.47407D+02,-5.08928D+01,1.43577D+02,
      *2.35807D+01,-5.11329D+01,-4.81020D-01,-1.78159D+00,5.64674D+00,
      *1.76457D+01,-2.21590D+01,-5.30303D+01,3.95325D+01,6.25844D+01,
      *-3.33397D+01,-2.54793D+01,1.08112D+01,-1.22138D+00,6.95454D-01,
      *1.43743D+01,1.26897D+01,-7.88189D+01,-5.39212D+01,1.74183D+02,
      *7.42545D+01,-1.69583D+02,-3.31767D+01,6.04830D+01,1.80525D-01,
      *9.49873D-01,-2.41311D+00,-8.22555D+00,9.34029D+00,2.41216D+01,
      *-1.66908D+01,-2.82084D+01,1.41353D+01,1.14375D+01,-4.60119D+00,
      *4.87451D-01,2.80142D-02,-5.98007D+00,-6.78124D+00,3.20509D+01,
      *2.57918D+01,-7.04560D+01,-3.41804D+01,6.85587D+01,1.49794D+01,
      *-2.44755D+01/
C     Z=5
       DATA A/
      *2.34678D+00,-2.45568D+00,9.39661D-01,4.44317D-01,-2.34527D-01,
      *-4.75024D-01,-2.77665D-01,1.95396D-01,3.31099D-01,-6.62374D-03,
      *-9.73365D-02,2.46355D-01,-4.45690D-01,-4.53208D-01,-1.67220D-01,
      *-1.63766D-01,-2.43292D-01,5.78079D-01,7.38401D-01,-2.57839D-01,
      *-3.28665D-01,2.02903D-02,-1.64637D-01,5.29196D-02,-5.76522D-01,
      *-3.94172D-01,1.72007D+00,1.25795D+00,-1.18922D+00,-1.05795D+00,
      *8.29497D-02,3.07707D-01,1.06764D-01,-5.06526D-02,-2.98836D-01,
      *6.78685D-01,1.41279D+00,1.21320D+00,-7.66964D-01,-8.22430D+00,
      *-5.78487D-01,1.08546D+01,3.59068D-01,-4.44364D+00,-2.52512D-01,
      *-2.38914D-01,4.42743D+00,2.25029D+00,-1.42436D+01,-5.48872D+00,
      *1.29541D+01,7.00458D+00,-1.08354D+00,-3.34977D+00,-2.10540D+00,
      *1.35888D-01,1.55859D+00,-1.54081D+00,-5.39881D+00,-8.56391D+00,
      *4.89452D+00,4.46932D+01,-1.25839D+00,-5.87190D+01,8.12964D-02,
      *2.41685D+01,8.95871D-01,1.58749D+00,-1.24010D+01,-8.00101D+00,
      *3.34644D+01,1.37775D+01,-1.21697D+01,-1.65474D+01,-2.76435D+01,
      *8.44970D+00,1.87229D+01,-2.52962D-02,-2.46381D+00,8.75166D-01,
      *7.78275D+00,1.73564D+01,-7.57342D+00,-7.26934D+01,2.59953D+00,
      *9.15278D+01,-3.29080D-01,-3.71138D+01,-9.22216D-01,-2.71821D+00,
      *1.33790D+01,1.10982D+01,-2.91143D+01,-1.60913D+01,-1.31671D+01,
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       DATA A/
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       DATA A/
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C     Z=13
       DATA A/
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       DATA A/
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       DATA A/
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       DATA A/
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       DATA A/
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